We use the resonant dipole-dipole interaction between Rydberg atoms and a periodic external microwave field to engineer XXZ spin Hamiltonians with tunable anisotropies. The are placed in one-dimensional (1D) two-dimensional (2D) arrays of optical tweezers. As illustrations, we apply this engineering two iconic situations physics: Heisenberg model square transport 1D. first benchmark Hamiltonian...

We consider a class of general spin Hamiltonians of the form Hs(t) = H0(t)+H ′(t) where H0(t) and H ′(t) describe the dipole interaction of the spins with an arbitrary time-dependent magnetic field and the internal interaction of the spins, respectively. We show that if H ′(t) is rotationally invariant, then Hs(t) admits the same dynamical invariant as H0(t). A direct application of this observ...

As a continuation of our previous work, we derive the optimal flux phase which minimizes the ground state energy in the one-dimensional many particle systems, when the number of particles is odd in the absence of on-site interaction and external potential. Moreover, we study the relationship between the flux on the ring and the spin of the ground state through which we derive some information o...

We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment of the usual formalism. In particular, we found explicit connections between quadratic Hamiltonians and Lagrangians, in their commutative and noncommutative r...

We suggest a sequence of instantaneous spin rotations, that reverses the time evolution of a spin subject to an arbitrary built-in magnetic field. The sequence does not require the knowledge of the direction or strength of the built-in field, and is applicable as long as that field is constant in time. The advantage of the suggested sequence compared to the known spin-echo sequences is that it ...

A local supersymmetric action for a (2+1)-dimensional system including gravity, the electromagnetic field and a Dirac spin-1/2 field is presented. The action is a Chern-Simons form for a connection of the OSp(2|2) group. All the fields enter as parts of the connection, that transforms in the adjoint representation of the gauge group. The system is off-shell invariant under local (gauge) supersy...

We construct the classical r-matrix structure for the Lax formulation of BC N Ruijsenaars-Schneider systems proposed in [18]. The r-matrix structure takes a quadratic form similar to the A N Ruijsenaars-Schneider Poisson bracket behavior, although the dy-namical dependence is more complicated. Commuting Hamiltonians stemming from the BC N Ruijsenaars-Schneider Lax matrix are shown to be linear ...

Spin and spatial tensor manipulations are frequently required to describe the theory of NMR experiments. A Mathematica package is presented here, which provides some of the most common functions for these calculations. Examples are the calculation of matrix representations of operators, commutators, projections, rotations, Redfield matrix elements, matrix decomposition into basis operators, cha...

We present a detailed study of the magnetic structure and spin waves in the Fe jarosite compound KFe3(SO4)2(OH)6 for the most general Hamiltonian involving oneand two-spin interactions which are allowed by symmetry. We compare the calculated spin-wave spectrum with the recent neutron scattering data of Matan et al. for various model Hamiltonians which include, in addition to isotropic Heisenber...